%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP777-10 : TPTP v9.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.LDl1VY7HiJ true
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:37:14 PM UTC 2025
% Result : Unsatisfiable 52.76s 8.22s
% Output : Refutation 52.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP777-10 : TPTP v9.2.0. Released v8.1.0.
% 0.10/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.LDl1VY7HiJ true
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 14:04:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.54/0.65 % Total configuration time : 435
% 0.54/0.65 % Estimated wc time : 1092
% 0.54/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 52.76/8.22 % Solved by fo/fo4.sh.
% 52.76/8.22 % done 1044 iterations in 7.453s
% 52.76/8.22 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 52.76/8.22 % SZS output start Refutation
% 52.76/8.22 thf(a_type, type, a: $i).
% 52.76/8.22 thf(b_type, type, b: $i).
% 52.76/8.22 thf(c_type, type, c: $i).
% 52.76/8.22 thf(bigC_type, type, bigC: $i > $i > $i > $i).
% 52.76/8.22 thf(product_type, type, product: $i > $i > $i).
% 52.76/8.22 thf(quotient_type, type, quotient: $i > $i > $i).
% 52.76/8.22 thf(x0_type, type, x0: $i).
% 52.76/8.22 thf(difference_type, type, difference: $i > $i > $i).
% 52.76/8.22 thf(goal, conjecture, (( bigC @ a @ b @ x0 ) = ( bigC @ c @ c @ x0 ))).
% 52.76/8.22 thf(zf_stmt_0, negated_conjecture,
% 52.76/8.22 (( bigC @ a @ b @ x0 ) != ( bigC @ c @ c @ x0 )),
% 52.76/8.22 inference('cnf.neg', [status(esa)], [goal])).
% 52.76/8.22 thf(zip_derived_cl9, plain, (((bigC @ a @ b @ x0) != (bigC @ c @ c @ x0))),
% 52.76/8.22 inference('cnf', [status(esa)], [zf_stmt_0])).
% 52.76/8.22 thf(sos09, axiom,
% 52.76/8.22 (( product @ ( product @ a @ c ) @ ( product @ c @ b ) ) =
% 52.76/8.22 ( product @ a @ b ))).
% 52.76/8.22 thf(zip_derived_cl8, plain,
% 52.76/8.22 (((product @ (product @ a @ c) @ (product @ c @ b)) = (product @ a @ b))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos09])).
% 52.76/8.22 thf(sos06, axiom, (( product @ A @ A ) = ( A ))).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(sos08, axiom,
% 52.76/8.22 (( bigC @ A @ B @ C ) =
% 52.76/8.22 ( product @ ( product @ A @ B ) @ ( product @ C @ A ) ))).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl23, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X0) = (product @ (product @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl169, plain,
% 52.76/8.22 (((bigC @ (product @ a @ c) @ (product @ c @ b) @ (product @ a @ c))
% 52.76/8.22 = (product @ (product @ a @ b) @ (product @ a @ c)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl23])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(sos05, axiom,
% 52.76/8.22 (( product @ ( product @ A @ B ) @ ( product @ C @ D ) ) =
% 52.76/8.22 ( product @ ( product @ A @ C ) @ ( product @ B @ D ) ))).
% 52.76/8.22 thf(zip_derived_cl4, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((product @ (product @ X0 @ X2) @ (product @ X1 @ X3))
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X3)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos05])).
% 52.76/8.22 thf(zip_derived_cl51, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X1 @ X0)
% 52.76/8.22 = (product @ (product @ X2 @ X0) @ (product @ X1 @ X2)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl520, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X0 @ X1) = (bigC @ X2 @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl27, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X0 @ X1) = (product @ X0 @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl7])).
% 52.76/8.22 thf(sos01, axiom, (( difference @ A @ ( product @ A @ B ) ) = ( B ))).
% 52.76/8.22 thf(zip_derived_cl0, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ X1 @ (product @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos01])).
% 52.76/8.22 thf(zip_derived_cl176, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ X1 @ (bigC @ X1 @ X1 @ X0)) = (product @ X0 @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl611, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ X0 @ (bigC @ X0 @ X1 @ X0)) = (product @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl520, zip_derived_cl176])).
% 52.76/8.22 thf(zip_derived_cl900, plain,
% 52.76/8.22 (((difference @ (product @ a @ c) @
% 52.76/8.22 (product @ (product @ a @ b) @ (product @ a @ c)))
% 52.76/8.22 = (product @ (product @ c @ b) @ (product @ a @ c)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl169, zip_derived_cl611])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl903, plain,
% 52.76/8.22 (((difference @ (product @ a @ c) @
% 52.76/8.22 (product @ (product @ a @ b) @ (product @ a @ c)))
% 52.76/8.22 = (bigC @ c @ b @ a))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl900, zip_derived_cl7])).
% 52.76/8.22 thf(sos02, axiom, (( product @ A @ ( difference @ A @ B ) ) = ( B ))).
% 52.76/8.22 thf(zip_derived_cl1, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ X1 @ (difference @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos02])).
% 52.76/8.22 thf(zip_derived_cl1102, plain,
% 52.76/8.22 (((product @ (product @ a @ c) @ (bigC @ c @ b @ a))
% 52.76/8.22 = (product @ (product @ a @ b) @ (product @ a @ c)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl903, zip_derived_cl1])).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(zip_derived_cl4, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((product @ (product @ X0 @ X2) @ (product @ X1 @ X3))
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X3)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos05])).
% 52.76/8.22 thf(zip_derived_cl58, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((product @ X0 @ (product @ X2 @ X1))
% 52.76/8.22 = (product @ (product @ X0 @ X2) @ (product @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl6766, plain,
% 52.76/8.22 (((product @ (product @ a @ c) @ (bigC @ c @ b @ a))
% 52.76/8.22 = (product @ a @ (product @ b @ c)))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl1102, zip_derived_cl58])).
% 52.76/8.22 thf(sos04, axiom, (( product @ ( quotient @ A @ B ) @ B ) = ( A ))).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl27, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X0 @ X1) = (product @ X0 @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl200, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X1 @ X1 @ (quotient @ X0 @ X1)) = (product @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl27])).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(zip_derived_cl51, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X1 @ X0)
% 52.76/8.22 = (product @ (product @ X2 @ X0) @ (product @ X1 @ X2)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl522, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X0 @ X1) = (product @ (product @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl51])).
% 52.76/8.22 thf(sos03, axiom, (( quotient @ ( product @ A @ B ) @ B ) = ( A ))).
% 52.76/8.22 thf(zip_derived_cl2, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ (product @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos03])).
% 52.76/8.22 thf(zip_derived_cl557, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (bigC @ X1 @ X1 @ X0) @ X1) = (product @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl522, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl861, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ X0) @ X1)
% 52.76/8.22 = (product @ X1 @ (quotient @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl557])).
% 52.76/8.22 thf(zip_derived_cl7145, plain,
% 52.76/8.22 (((quotient @ (product @ a @ (product @ b @ c)) @ (product @ a @ c))
% 52.76/8.22 = (product @ (product @ a @ c) @
% 52.76/8.22 (quotient @ (bigC @ c @ b @ a) @ (product @ a @ c))))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl6766, zip_derived_cl861])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl2, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ (product @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos03])).
% 52.76/8.22 thf(zip_derived_cl19, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((quotient @ (bigC @ X2 @ X1 @ X0) @ (product @ X0 @ X2))
% 52.76/8.22 = (product @ X2 @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl8, plain,
% 52.76/8.22 (((product @ (product @ a @ c) @ (product @ c @ b)) = (product @ a @ b))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos09])).
% 52.76/8.22 thf(zip_derived_cl7198, plain,
% 52.76/8.22 (((quotient @ (product @ a @ (product @ b @ c)) @ (product @ a @ c))
% 52.76/8.22 = (product @ a @ b))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl7145, zip_derived_cl19, zip_derived_cl8])).
% 52.76/8.22 thf(zip_derived_cl6766, plain,
% 52.76/8.22 (((product @ (product @ a @ c) @ (bigC @ c @ b @ a))
% 52.76/8.22 = (product @ a @ (product @ b @ c)))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl1102, zip_derived_cl58])).
% 52.76/8.22 thf(zip_derived_cl8, plain,
% 52.76/8.22 (((product @ (product @ a @ c) @ (product @ c @ b)) = (product @ a @ b))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos09])).
% 52.76/8.22 thf(sos07, axiom,
% 52.76/8.22 (( product @
% 52.76/8.22 ( product @ ( product @ A @ B ) @ B ) @
% 52.76/8.22 ( product @ B @ ( product @ B @ A ) ) ) =
% 52.76/8.22 ( B ))).
% 52.76/8.22 thf(zip_derived_cl6, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (product @ (product @ X1 @ X0) @ X0) @
% 52.76/8.22 (product @ X0 @ (product @ X0 @ X1))) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos07])).
% 52.76/8.22 thf(zip_derived_cl133, plain,
% 52.76/8.22 (((product @ (product @ (product @ a @ b) @ (product @ c @ b)) @
% 52.76/8.22 (product @ (product @ c @ b) @
% 52.76/8.22 (product @ (product @ c @ b) @ (product @ a @ c))))
% 52.76/8.22 = (product @ c @ b))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 52.76/8.22 thf(zip_derived_cl4, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((product @ (product @ X0 @ X2) @ (product @ X1 @ X3))
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X3)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos05])).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl145, plain,
% 52.76/8.22 (((product @ (product @ (product @ a @ c) @ b) @
% 52.76/8.22 (product @ (product @ c @ b) @ (bigC @ c @ b @ a)))
% 52.76/8.22 = (product @ c @ b))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl133, zip_derived_cl4, zip_derived_cl5,
% 52.76/8.22 zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl4, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((product @ (product @ X0 @ X2) @ (product @ X1 @ X3))
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X3)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos05])).
% 52.76/8.22 thf(zip_derived_cl0, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ X1 @ (product @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos01])).
% 52.76/8.22 thf(zip_derived_cl34, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((difference @ (product @ X3 @ X1) @
% 52.76/8.22 (product @ (product @ X3 @ X2) @ (product @ X1 @ X0)))
% 52.76/8.22 = (product @ X2 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl2285, plain,
% 52.76/8.22 (((difference @ (product @ (product @ a @ c) @ (product @ c @ b)) @
% 52.76/8.22 (product @ c @ b)) = (product @ b @ (bigC @ c @ b @ a)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl145, zip_derived_cl34])).
% 52.76/8.22 thf(zip_derived_cl8, plain,
% 52.76/8.22 (((product @ (product @ a @ c) @ (product @ c @ b)) = (product @ a @ b))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos09])).
% 52.76/8.22 thf(zip_derived_cl2378, plain,
% 52.76/8.22 (((difference @ (product @ a @ b) @ (product @ c @ b))
% 52.76/8.22 = (product @ b @ (bigC @ c @ b @ a)))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl2285, zip_derived_cl8])).
% 52.76/8.22 thf(zip_derived_cl1, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ X1 @ (difference @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos02])).
% 52.76/8.22 thf(zip_derived_cl2, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ (product @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos03])).
% 52.76/8.22 thf(zip_derived_cl14, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ X0 @ (difference @ X1 @ X0)) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl2381, plain,
% 52.76/8.22 (((quotient @ (product @ c @ b) @ (product @ b @ (bigC @ c @ b @ a)))
% 52.76/8.22 = (product @ a @ b))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl2378, zip_derived_cl14])).
% 52.76/8.22 thf(zip_derived_cl861, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ X0) @ X1)
% 52.76/8.22 = (product @ X1 @ (quotient @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl557])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl904, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (product @ X0 @ (quotient @ X1 @ X0)) @ X0)
% 52.76/8.22 = (product @ X0 @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl861, zip_derived_cl3])).
% 52.76/8.22 thf(zip_derived_cl2616, plain,
% 52.76/8.22 (((product @
% 52.76/8.22 (product @ (product @ b @ (bigC @ c @ b @ a)) @ (product @ a @ b)) @
% 52.76/8.22 (product @ b @ (bigC @ c @ b @ a)))
% 52.76/8.22 = (product @ (product @ b @ (bigC @ c @ b @ a)) @ (product @ c @ b)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl2381, zip_derived_cl904])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl520, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X0 @ X1) = (bigC @ X2 @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl520, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X0 @ X1) = (bigC @ X2 @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl2633, plain,
% 52.76/8.22 (((product @ (bigC @ b @ a @ (bigC @ c @ b @ a)) @
% 52.76/8.22 (product @ b @ (bigC @ c @ b @ a)))
% 52.76/8.22 = (bigC @ b @ c @ (bigC @ c @ b @ a)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl2616, zip_derived_cl7, zip_derived_cl520,
% 52.76/8.22 zip_derived_cl7, zip_derived_cl520])).
% 52.76/8.22 thf(zip_derived_cl2381, plain,
% 52.76/8.22 (((quotient @ (product @ c @ b) @ (product @ b @ (bigC @ c @ b @ a)))
% 52.76/8.22 = (product @ a @ b))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl2378, zip_derived_cl14])).
% 52.76/8.22 thf(zip_derived_cl1, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ X1 @ (difference @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos02])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl24, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ (difference @ X1 @ X0) @ X2 @ X1)
% 52.76/8.22 = (product @ (product @ (difference @ X1 @ X0) @ X2) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl1, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ X1 @ (difference @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos02])).
% 52.76/8.22 thf(zip_derived_cl6, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (product @ (product @ X1 @ X0) @ X0) @
% 52.76/8.22 (product @ X0 @ (product @ X0 @ X1))) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos07])).
% 52.76/8.22 thf(zip_derived_cl2, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ (product @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos03])).
% 52.76/8.22 thf(zip_derived_cl104, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ X0 @ (product @ X0 @ (product @ X0 @ X1)))
% 52.76/8.22 = (product @ (product @ X1 @ X0) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl7303, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ X1 @ (product @ X1 @ X0))
% 52.76/8.22 = (product @ (product @ (difference @ X1 @ X0) @ X1) @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl104])).
% 52.76/8.22 thf(zip_derived_cl1, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ X1 @ (difference @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos02])).
% 52.76/8.22 thf(zip_derived_cl522, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X0 @ X1) = (product @ (product @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl51])).
% 52.76/8.22 thf(zip_derived_cl581, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X1 @ X1 @ (difference @ X1 @ X0)) = (product @ X0 @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl522])).
% 52.76/8.22 thf(zip_derived_cl176, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ X1 @ (bigC @ X1 @ X1 @ X0)) = (product @ X0 @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl869, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ X0 @ (product @ X1 @ X0))
% 52.76/8.22 = (product @ (difference @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl581, zip_derived_cl176])).
% 52.76/8.22 thf(zip_derived_cl869, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ X0 @ (product @ X1 @ X0))
% 52.76/8.22 = (product @ (difference @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl581, zip_derived_cl176])).
% 52.76/8.22 thf(zip_derived_cl7362, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ X1 @ (product @ X1 @ X0))
% 52.76/8.22 = (difference @ X1 @ (product @ (product @ X0 @ X1) @ X1)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl7303, zip_derived_cl869, zip_derived_cl869])).
% 52.76/8.22 thf(zip_derived_cl23, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X0) = (product @ (product @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl6, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (product @ (product @ X1 @ X0) @ X0) @
% 52.76/8.22 (product @ X0 @ (product @ X0 @ X1))) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos07])).
% 52.76/8.22 thf(zip_derived_cl0, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ X1 @ (product @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos01])).
% 52.76/8.22 thf(zip_derived_cl102, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ (product @ (product @ X1 @ X0) @ X0) @ X0)
% 52.76/8.22 = (product @ X0 @ (product @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl7079, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ (product @ X0 @ X1) @ X1)
% 52.76/8.22 = (product @ X1 @ (product @ X1 @ (quotient @ X0 @ X1))))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl102])).
% 52.76/8.22 thf(zip_derived_cl861, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ X0) @ X1)
% 52.76/8.22 = (product @ X1 @ (quotient @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl557])).
% 52.76/8.22 thf(zip_derived_cl9680, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (difference @ (product @ X1 @ X0) @ X0) @ X0)
% 52.76/8.22 = (product @ X0 @
% 52.76/8.22 (quotient @ (product @ X0 @ (quotient @ X1 @ X0)) @ X0)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl7079, zip_derived_cl861])).
% 52.76/8.22 thf(zip_derived_cl861, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ X0) @ X1)
% 52.76/8.22 = (product @ X1 @ (quotient @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl557])).
% 52.76/8.22 thf(zip_derived_cl7079, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ (product @ X0 @ X1) @ X1)
% 52.76/8.22 = (product @ X1 @ (product @ X1 @ (quotient @ X0 @ X1))))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl102])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl9816, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (difference @ (product @ X1 @ X0) @ X0) @ X0)
% 52.76/8.22 = (difference @ X1 @ X0))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl9680, zip_derived_cl861, zip_derived_cl7079,
% 52.76/8.22 zip_derived_cl3])).
% 52.76/8.22 thf(zip_derived_cl9904, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (difference @ X0 @ X1) @ X1)
% 52.76/8.22 = (difference @ (quotient @ X0 @ X1) @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl9816])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl10091, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (difference @ (quotient @ X1 @ X0) @ X0) @ X0)
% 52.76/8.22 = (difference @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl9904, zip_derived_cl3])).
% 52.76/8.22 thf(zip_derived_cl1, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ X1 @ (difference @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos02])).
% 52.76/8.22 thf(zip_derived_cl58, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((product @ X0 @ (product @ X2 @ X1))
% 52.76/8.22 = (product @ (product @ X0 @ X2) @ (product @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl6917, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((product @ X2 @ (product @ (difference @ X2 @ X0) @ X1))
% 52.76/8.22 = (product @ X0 @ (product @ X2 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl58])).
% 52.76/8.22 thf(zip_derived_cl11007, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (quotient @ X1 @ X0) @ (difference @ X1 @ X0))
% 52.76/8.22 = (product @ X0 @ (product @ (quotient @ X1 @ X0) @ X0)))),
% 52.76/8.22 inference('sup+', [status(thm)],
% 52.76/8.22 [zip_derived_cl10091, zip_derived_cl6917])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl11077, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (quotient @ X1 @ X0) @ (difference @ X1 @ X0))
% 52.76/8.22 = (product @ X0 @ X1))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl11007, zip_derived_cl3])).
% 52.76/8.22 thf(zip_derived_cl2, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ (product @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos03])).
% 52.76/8.22 thf(zip_derived_cl11913, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ X0) @ (difference @ X0 @ X1))
% 52.76/8.22 = (quotient @ X0 @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl11077, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl12935, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (bigC @ X0 @ X1 @ X0) @
% 52.76/8.22 (difference @ X0 @ (product @ X0 @ X1)))
% 52.76/8.22 = (quotient @ X0 @ (product @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl11913])).
% 52.76/8.22 thf(zip_derived_cl0, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ X1 @ (product @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos01])).
% 52.76/8.22 thf(zip_derived_cl13024, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (bigC @ X0 @ X1 @ X0) @ X1)
% 52.76/8.22 = (quotient @ X0 @ (product @ X0 @ X1)))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl12935, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl11077, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (quotient @ X1 @ X0) @ (difference @ X1 @ X0))
% 52.76/8.22 = (product @ X0 @ X1))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl11007, zip_derived_cl3])).
% 52.76/8.22 thf(zip_derived_cl1, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ X1 @ (difference @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos02])).
% 52.76/8.22 thf(zip_derived_cl58, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((product @ X0 @ (product @ X2 @ X1))
% 52.76/8.22 = (product @ (product @ X0 @ X2) @ (product @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl6871, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((product @ X1 @ (product @ X2 @ (difference @ X1 @ X0)))
% 52.76/8.22 = (product @ (product @ X1 @ X2) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl58])).
% 52.76/8.22 thf(zip_derived_cl11961, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X0 @ (product @ X1 @ X0))
% 52.76/8.22 = (product @ (product @ X0 @ (quotient @ X0 @ X1)) @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)],
% 52.76/8.22 [zip_derived_cl11077, zip_derived_cl6871])).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(zip_derived_cl51, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X1 @ X0)
% 52.76/8.22 = (product @ (product @ X2 @ X0) @ (product @ X1 @ X2)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl536, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X0) = (product @ X0 @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl51])).
% 52.76/8.22 thf(zip_derived_cl12118, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X0)
% 52.76/8.22 = (product @ (product @ X0 @ (quotient @ X0 @ X1)) @ X1))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl11961, zip_derived_cl536])).
% 52.76/8.22 thf(zip_derived_cl2, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ (product @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos03])).
% 52.76/8.22 thf(zip_derived_cl14569, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (bigC @ X0 @ X1 @ X0) @ X1)
% 52.76/8.22 = (product @ X0 @ (quotient @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl12118, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl15262, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X0 @ (quotient @ X0 @ X1))
% 52.76/8.22 = (quotient @ X0 @ (product @ X0 @ X1)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl13024, zip_derived_cl14569])).
% 52.76/8.22 thf(zip_derived_cl19796, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ (quotient @ X1 @ X0))
% 52.76/8.22 = (difference @ X1 @ (product @ (product @ X0 @ X1) @ X1)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl7362, zip_derived_cl15262])).
% 52.76/8.22 thf(zip_derived_cl19826, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ (quotient @ X1 @ (difference @ X0 @ X1)))
% 52.76/8.22 = (difference @ X1 @ (bigC @ (difference @ X0 @ X1) @ X1 @ X0)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl19796])).
% 52.76/8.22 thf(zip_derived_cl14, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ X0 @ (difference @ X1 @ X0)) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl19935, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ X0)
% 52.76/8.22 = (difference @ X1 @ (bigC @ (difference @ X0 @ X1) @ X1 @ X0)))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl19826, zip_derived_cl14])).
% 52.76/8.22 thf(zip_derived_cl1, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ X1 @ (difference @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos02])).
% 52.76/8.22 thf(zip_derived_cl20342, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ (product @ X1 @ X0))
% 52.76/8.22 = (bigC @ (difference @ X0 @ X1) @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl19935, zip_derived_cl1])).
% 52.76/8.22 thf(zip_derived_cl51, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X1 @ X0)
% 52.76/8.22 = (product @ (product @ X2 @ X0) @ (product @ X1 @ X2)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl2, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ (product @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos03])).
% 52.76/8.22 thf(zip_derived_cl497, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((quotient @ (bigC @ X2 @ X1 @ X0) @ (product @ X1 @ X2))
% 52.76/8.22 = (product @ X2 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl20518, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ (product @ X1 @ X0)) @
% 52.76/8.22 (product @ X1 @ (difference @ X0 @ X1)))
% 52.76/8.22 = (product @ (difference @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl20342, zip_derived_cl497])).
% 52.76/8.22 thf(zip_derived_cl14, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ X0 @ (difference @ X1 @ X0)) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl15262, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X0 @ (quotient @ X0 @ X1))
% 52.76/8.22 = (quotient @ X0 @ (product @ X0 @ X1)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl13024, zip_derived_cl14569])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl0, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ X1 @ (product @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos01])).
% 52.76/8.22 thf(zip_derived_cl15, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ (quotient @ X0 @ X1) @ X0) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl15331, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ (product @ X1 @ (quotient @ X1 @ X0)) @ X1)
% 52.76/8.22 = (product @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl15262, zip_derived_cl15])).
% 52.76/8.22 thf(zip_derived_cl16583, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ (product @ X1 @ X0) @ X1)
% 52.76/8.22 = (product @ X1 @ (difference @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl15331])).
% 52.76/8.22 thf(zip_derived_cl11913, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ X0) @ (difference @ X0 @ X1))
% 52.76/8.22 = (quotient @ X0 @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl11077, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl861, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ X0) @ X1)
% 52.76/8.22 = (product @ X1 @ (quotient @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl557])).
% 52.76/8.22 thf(zip_derived_cl869, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ X0 @ (product @ X1 @ X0))
% 52.76/8.22 = (product @ (difference @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl581, zip_derived_cl176])).
% 52.76/8.22 thf(zip_derived_cl20658, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ (quotient @ X0 @ X1))
% 52.76/8.22 = (difference @ X0 @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl20518, zip_derived_cl16583,
% 52.76/8.22 zip_derived_cl11913, zip_derived_cl861, zip_derived_cl869])).
% 52.76/8.22 thf(zip_derived_cl20938, plain,
% 52.76/8.22 (((product @ (product @ b @ (bigC @ c @ b @ a)) @ (product @ a @ b))
% 52.76/8.22 = (difference @ (product @ c @ b) @
% 52.76/8.22 (product @ (product @ b @ (bigC @ c @ b @ a)) @ (product @ c @ b))))),
% 52.76/8.22 inference('sup+', [status(thm)],
% 52.76/8.22 [zip_derived_cl2381, zip_derived_cl20658])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl520, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X0 @ X1) = (bigC @ X2 @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl520, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X0 @ X1) = (bigC @ X2 @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl2378, plain,
% 52.76/8.22 (((difference @ (product @ a @ b) @ (product @ c @ b))
% 52.76/8.22 = (product @ b @ (bigC @ c @ b @ a)))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl2285, zip_derived_cl8])).
% 52.76/8.22 thf(zip_derived_cl9816, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (difference @ (product @ X1 @ X0) @ X0) @ X0)
% 52.76/8.22 = (difference @ X1 @ X0))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl9680, zip_derived_cl861, zip_derived_cl7079,
% 52.76/8.22 zip_derived_cl3])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl9840, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (difference @ X1 @ X0) @ X0)
% 52.76/8.22 = (difference @ (product @ X1 @ X0) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl9816, zip_derived_cl3])).
% 52.76/8.22 thf(zip_derived_cl10023, plain,
% 52.76/8.22 (((product @ (product @ b @ (bigC @ c @ b @ a)) @ (product @ c @ b))
% 52.76/8.22 = (difference @ (product @ (product @ a @ b) @ (product @ c @ b)) @
% 52.76/8.22 (product @ c @ b)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl2378, zip_derived_cl9840])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl520, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X2 @ X0 @ X1) = (bigC @ X2 @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl4, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((product @ (product @ X0 @ X2) @ (product @ X1 @ X3))
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X3)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos05])).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(zip_derived_cl145, plain,
% 52.76/8.22 (((product @ (product @ (product @ a @ c) @ b) @
% 52.76/8.22 (product @ (product @ c @ b) @ (bigC @ c @ b @ a)))
% 52.76/8.22 = (product @ c @ b))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl133, zip_derived_cl4, zip_derived_cl5,
% 52.76/8.22 zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl0, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ X1 @ (product @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos01])).
% 52.76/8.22 thf(zip_derived_cl231, plain,
% 52.76/8.22 (((difference @ (product @ (product @ a @ c) @ b) @ (product @ c @ b))
% 52.76/8.22 = (product @ (product @ c @ b) @ (bigC @ c @ b @ a)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl145, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl10060, plain,
% 52.76/8.22 (((bigC @ b @ c @ (bigC @ c @ b @ a))
% 52.76/8.22 = (product @ (product @ c @ b) @ (bigC @ c @ b @ a)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl10023, zip_derived_cl7, zip_derived_cl520,
% 52.76/8.22 zip_derived_cl4, zip_derived_cl5, zip_derived_cl231])).
% 52.76/8.22 thf(zip_derived_cl0, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ X1 @ (product @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos01])).
% 52.76/8.22 thf(zip_derived_cl10160, plain,
% 52.76/8.22 (((difference @ (product @ c @ b) @ (bigC @ b @ c @ (bigC @ c @ b @ a)))
% 52.76/8.22 = (bigC @ c @ b @ a))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl10060, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl21012, plain,
% 52.76/8.22 (((bigC @ b @ a @ (bigC @ c @ b @ a)) = (bigC @ c @ b @ a))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl20938, zip_derived_cl7, zip_derived_cl520,
% 52.76/8.22 zip_derived_cl7, zip_derived_cl520, zip_derived_cl10160])).
% 52.76/8.22 thf(zip_derived_cl536, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X0) = (product @ X0 @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl51])).
% 52.76/8.22 thf(zip_derived_cl21077, plain,
% 52.76/8.22 (((bigC @ (bigC @ c @ b @ a) @ b @ (bigC @ c @ b @ a))
% 52.76/8.22 = (bigC @ b @ c @ (bigC @ c @ b @ a)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl2633, zip_derived_cl21012, zip_derived_cl536])).
% 52.76/8.22 thf(zip_derived_cl19, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((quotient @ (bigC @ X2 @ X1 @ X0) @ (product @ X0 @ X2))
% 52.76/8.22 = (product @ X2 @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl21278, plain,
% 52.76/8.22 (((quotient @ (bigC @ b @ c @ (bigC @ c @ b @ a)) @
% 52.76/8.22 (product @ (bigC @ c @ b @ a) @ (bigC @ c @ b @ a)))
% 52.76/8.22 = (product @ (bigC @ c @ b @ a) @ b))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl21077, zip_derived_cl19])).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(zip_derived_cl10060, plain,
% 52.76/8.22 (((bigC @ b @ c @ (bigC @ c @ b @ a))
% 52.76/8.22 = (product @ (product @ c @ b) @ (bigC @ c @ b @ a)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl10023, zip_derived_cl7, zip_derived_cl520,
% 52.76/8.22 zip_derived_cl4, zip_derived_cl5, zip_derived_cl231])).
% 52.76/8.22 thf(zip_derived_cl2, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ (product @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos03])).
% 52.76/8.22 thf(zip_derived_cl10185, plain,
% 52.76/8.22 (((quotient @ (bigC @ b @ c @ (bigC @ c @ b @ a)) @ (bigC @ c @ b @ a))
% 52.76/8.22 = (product @ c @ b))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl10060, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl21295, plain,
% 52.76/8.22 (((product @ c @ b) = (product @ (bigC @ c @ b @ a) @ b))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl21278, zip_derived_cl5, zip_derived_cl10185])).
% 52.76/8.22 thf(zip_derived_cl200, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X1 @ X1 @ (quotient @ X0 @ X1)) = (product @ X1 @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl27])).
% 52.76/8.22 thf(zip_derived_cl522, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X0 @ X1) = (product @ (product @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl51])).
% 52.76/8.22 thf(zip_derived_cl0, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ X1 @ (product @ X1 @ X0)) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos01])).
% 52.76/8.22 thf(zip_derived_cl554, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ (product @ X1 @ X0) @ (bigC @ X1 @ X1 @ X0)) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl522, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl824, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ (product @ X1 @ (quotient @ X0 @ X1)) @
% 52.76/8.22 (product @ X1 @ X0)) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl554])).
% 52.76/8.22 thf(zip_derived_cl21326, plain,
% 52.76/8.22 (((difference @
% 52.76/8.22 (product @ (bigC @ c @ b @ a) @ (quotient @ b @ (bigC @ c @ b @ a))) @
% 52.76/8.22 (product @ c @ b)) = (bigC @ c @ b @ a))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl21295, zip_derived_cl824])).
% 52.76/8.22 thf(zip_derived_cl20658, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ (quotient @ X0 @ X1))
% 52.76/8.22 = (difference @ X0 @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl20518, zip_derived_cl16583,
% 52.76/8.22 zip_derived_cl11913, zip_derived_cl861, zip_derived_cl869])).
% 52.76/8.22 thf(zip_derived_cl21295, plain,
% 52.76/8.22 (((product @ c @ b) = (product @ (bigC @ c @ b @ a) @ b))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl21278, zip_derived_cl5, zip_derived_cl10185])).
% 52.76/8.22 thf(zip_derived_cl20658, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ (quotient @ X0 @ X1))
% 52.76/8.22 = (difference @ X0 @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl20518, zip_derived_cl16583,
% 52.76/8.22 zip_derived_cl11913, zip_derived_cl861, zip_derived_cl869])).
% 52.76/8.22 thf(zip_derived_cl824, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ (product @ X1 @ (quotient @ X0 @ X1)) @
% 52.76/8.22 (product @ X1 @ X0)) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl554])).
% 52.76/8.22 thf(zip_derived_cl21409, plain, (((c) = (bigC @ c @ b @ a))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl21326, zip_derived_cl20658,
% 52.76/8.22 zip_derived_cl21295, zip_derived_cl20658, zip_derived_cl824])).
% 52.76/8.22 thf(zip_derived_cl21460, plain,
% 52.76/8.22 (((product @ (product @ a @ c) @ c) = (product @ a @ (product @ b @ c)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl6766, zip_derived_cl21409])).
% 52.76/8.22 thf(zip_derived_cl861, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ (product @ X1 @ X0) @ X1)
% 52.76/8.22 = (product @ X1 @ (quotient @ X0 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl557])).
% 52.76/8.22 thf(zip_derived_cl15, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((difference @ (quotient @ X0 @ X1) @ X0) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 52.76/8.22 thf(zip_derived_cl9840, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ (difference @ X1 @ X0) @ X0)
% 52.76/8.22 = (difference @ (product @ X1 @ X0) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl9816, zip_derived_cl3])).
% 52.76/8.22 thf(zip_derived_cl10038, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X0 @ X1)
% 52.76/8.22 = (difference @ (product @ (quotient @ X1 @ X0) @ X1) @ X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl9840])).
% 52.76/8.22 thf(zip_derived_cl14, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((quotient @ X0 @ (difference @ X1 @ X0)) = (X1))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 52.76/8.22 thf(zip_derived_cl10745, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((quotient @ X0 @ (product @ X1 @ X0))
% 52.76/8.22 = (product @ (quotient @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl10038, zip_derived_cl14])).
% 52.76/8.22 thf(zip_derived_cl5, plain, (![X0 : $i]: ((product @ X0 @ X0) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos06])).
% 52.76/8.22 thf(zip_derived_cl4, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((product @ (product @ X0 @ X2) @ (product @ X1 @ X3))
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X3)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos05])).
% 52.76/8.22 thf(zip_derived_cl52, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((product @ (product @ X2 @ X1) @ X0)
% 52.76/8.22 = (product @ (product @ X2 @ X0) @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl20658, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ (quotient @ X0 @ X1))
% 52.76/8.22 = (difference @ X0 @ (product @ X1 @ X0)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl20518, zip_derived_cl16583,
% 52.76/8.22 zip_derived_cl11913, zip_derived_cl861, zip_derived_cl869])).
% 52.76/8.22 thf(zip_derived_cl869, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((difference @ X0 @ (product @ X1 @ X0))
% 52.76/8.22 = (product @ (difference @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl581, zip_derived_cl176])).
% 52.76/8.22 thf(zip_derived_cl19796, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((product @ X1 @ (quotient @ X1 @ X0))
% 52.76/8.22 = (difference @ X1 @ (product @ (product @ X0 @ X1) @ X1)))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl7362, zip_derived_cl15262])).
% 52.76/8.22 thf(zip_derived_cl22164, plain,
% 52.76/8.22 (((product @ c @ (quotient @ c @ a)) = (product @ a @ b))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl7198, zip_derived_cl21460, zip_derived_cl861,
% 52.76/8.22 zip_derived_cl10745, zip_derived_cl52, zip_derived_cl20658,
% 52.76/8.22 zip_derived_cl869, zip_derived_cl19796])).
% 52.76/8.22 thf(zip_derived_cl3, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]: ((product @ (quotient @ X0 @ X1) @ X1) = (X0))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos04])).
% 52.76/8.22 thf(zip_derived_cl4, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((product @ (product @ X0 @ X2) @ (product @ X1 @ X3))
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X3)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos05])).
% 52.76/8.22 thf(zip_derived_cl57, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 52.76/8.22 ((product @ (product @ X3 @ X2) @ X0)
% 52.76/8.22 = (product @ (product @ X3 @ (quotient @ X0 @ X1)) @
% 52.76/8.22 (product @ X2 @ X1)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 52.76/8.22 thf(zip_derived_cl23868, plain,
% 52.76/8.22 (![X0 : $i]:
% 52.76/8.22 ((product @ (product @ c @ X0) @ c)
% 52.76/8.22 = (product @ (product @ a @ b) @ (product @ X0 @ a)))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl22164, zip_derived_cl57])).
% 52.76/8.22 thf(zip_derived_cl522, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X0 @ X1) = (product @ (product @ X0 @ X1) @ X0))),
% 52.76/8.22 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl51])).
% 52.76/8.22 thf(zip_derived_cl7, plain,
% 52.76/8.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 52.76/8.22 ((bigC @ X0 @ X1 @ X2)
% 52.76/8.22 = (product @ (product @ X0 @ X1) @ (product @ X2 @ X0)))),
% 52.76/8.22 inference('cnf', [status(esa)], [sos08])).
% 52.76/8.22 thf(zip_derived_cl23913, plain,
% 52.76/8.22 (![X0 : $i]: ((bigC @ c @ c @ X0) = (bigC @ a @ b @ X0))),
% 52.76/8.22 inference('demod', [status(thm)],
% 52.76/8.22 [zip_derived_cl23868, zip_derived_cl522, zip_derived_cl7])).
% 52.76/8.22 thf(zip_derived_cl24085, plain,
% 52.76/8.22 (((bigC @ c @ c @ x0) != (bigC @ c @ c @ x0))),
% 52.76/8.22 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl23913])).
% 52.76/8.22 thf(zip_derived_cl24086, plain, ($false),
% 52.76/8.22 inference('simplify', [status(thm)], [zip_derived_cl24085])).
% 52.76/8.22
% 52.76/8.22 % SZS output end Refutation
% 52.76/8.22
% 52.76/8.22
% 52.76/8.22 % Terminating...
% 53.42/8.28 % Runner terminated.
% 53.42/8.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------